Linearity criteria for automorphism groups of malabelian groups

Abstract

Let $G$ be a finitely generated malabelian group, let $A\le \mathrm{Out}(G)$ be a finitely generated subgroup, and let ${\Gamma }_{G,A}$ denote the preimage of $A$ in $\mathrm{Aut}(G)$. We give a general criterion for the linearity of ${\Gamma }_{G,A}$ in terms of surjections from $G$ to finite simple groups of Lie type.

28 pages. To appear in Math. Annalen